A variation of constants formula and Bellman-Gronwall-Reid inequalities

DOI10.1016/0022-247X(73)90195-9zbMath0251.34009MaRDI QIDQ2556967

Vangipuram Lakshmikantham

Publication date: 1973

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Differential inequalities involving functions of a single real variable (34A40)

Related Items (13)

About some new integral inequalities of wendroff type for discontinuous functions ⋮ A new approach to the stability theory of functional differential systems ⋮ A new approach to the stability theory of functional differential systems ⋮ Integro-sum inequalities and motion stability of systems with impulse perturbations ⋮ On some generalizations o f Bellman's lemma ⋮ The Lyapunov matrix-function ⋮ A note on Gronwall-Bellman inequality ⋮ A nonlinear variation of constants method for integro differential and integral equations ⋮ A new approach to the method of nonlinear variation of parameters ⋮ Method of integral inequalities in the theory of stability of motion ⋮ A brief biography and survey of collected works of V. Lakshmikantham ⋮ Perturbation of functional-differential equations with nonuniform stability behavior ⋮ Error estimates of solutions and mean of solutions of stochastic differential systems

Cites Work

• A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations
• A Note on a Functional Inequality
• A Note on Gronwall's Inequality
• Unnamed Item

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